W is the set of all vectors in R2 whose second component is

W is the set of all vectors in R^2 whose second component is the square of the first. W is not a subspace of R^2. Verify this by giving a specific example that violates the test for a vector subspace.

Consider two elements in W: (1,1),(2,4)

(1,1)+(2,4)=(1+2,1+4)=(3,5)

Second component is 5 which is not a square of 3. Hence, sum of these two elements in W does not belong in W. Hence W is not subspace of R2

W is the set of all vectors in R^2 whose second component is the square of the first. W is not a subspace of R^2. Verify this by giving a specific example that

W is the set of all vectors in R2 whose second component is

Solution

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